SECTION 1. — Of the Nature of Flatland

I call our world Flatland, not because we call it so, but to make
its nature clearer to you, my happy readers, who are privileged to
live in Space.

Imagine a vast sheet of paper on which straight Lines, Triangles,
Squares, Pentagons, Hexagons, and other figures, instead of remaining
fixed in their places, move freely about, on or in the surface, but
without the power of rising above or sinking below it, very much like
shadows — only hard with luminous edges — and you will then have a
pretty correct notion of my country and countrymen. Alas, a few years
ago, I should have said “my universe”: but now my mind has been
opened to higher views of things.

In such a country, you will perceive at once that it is impossible
that there should be anything of what you call a “solid” kind; but I
dare say you will suppose that we could at least distinguish by sight
the Triangles, Squares, and other figures, moving about as I have
described them. On the contrary, we could see nothing of the kind,
not at least so as to distinguish one figure from another. Nothing
was visible, nor could be visible, to us, except Straight Lines; and
the necessity of this I will speedily demonstrate.

Place a penny on the middle of one of your tables in Space; and
leaning over it, look down upon it. It will appear a circle.

But now, drawling back to the edge of the table, gradually lower
your eye (thus bringing yourself more and more into the condition of
the inhabitants of Flatland), and you will find the penny becoming
more and more oval to your view, and at last when you have placed your
eye exactly on the edge of the table (so that you are, as it were,
actually a Flatlander) the penny will then have ceased to appear oval
at all, and will have become, so far as you can see, a straight line.

The same thing would happen if you were to treat in the same way a
Triangle, or a Square, or any other figure cut out of pasteboard.
As soon as you look at it with your eye on the edge of the table, you
will find that it ceases to appear to you as a figure, and that it
becomes in appearance a straight line. Take for example an
equilateral Triangle — who represents with us a Tradesman of the
respectable class. Figure 1 represents the Tradesman as you would see
him while you were bending over him from above; figures 2 and 3
represent the Tradesman, as you would see him if your eye were close
to the level, or all but on the level of the table; and if your eye
were quite on the level of the table (and that is how we see him in
Flatland) you would see nothing but a straight line.

Figure 1

When I was in Spaceland I heard that your sailors have very
similar experiences while they traverse your seas and discern some
distant island or coast lying on the horizon. The far-off land may
have bays, forelands, angles in and out to any number and extent; yet
at a distance you see none of these (unless indeed your sun shines
bright upon them revealing the projections and retirements by means of
light and shade), nothing but a grey unbroken line upon the water.

Well, that is just what we see when one of our triangular or other
acquaintances comes towards us in Flatland. As there is neither sun
with us, nor any light of such a kind as to make shadows, we have none
of the helps to the sight that you have in Spaceland. If our friend
comes closer to us we see his line becomes larger; if he leaves us it
becomes smaller; but still he looks like a straight line; be he a
Triangle, Square, Pentagon, Hexagon, Circle, what you will — a
straight Line he looks and nothing else.

You may perhaps ask how under these disadvantageous circumstances we
are able to distinguish our friends from one another: but the answer
to this very natural question will be more fitly and easily given when
I come to describe the inhabitants of Flatland. For the present let
me defer this subject, and say a word or two about the climate and
houses in our country.